• A FIXED POINT THEOREM ON PRODUCT OF METRIC SPACES

U. C. GAIROLA, DEEPAK KHANTWAL*

Abstract


J. Matkowski [19], gave an important generalization of Banach contraction principle for a finite product of metric spaces. This result has been extended and generalized by several mathematicians. Recently Pant [22] gave an important concept of reciprocal continuity for a pair of maps. In this paper, we introduced the coordinatewise reciprocal continuity and proved a fixed point theorem which extend and unify the result of Jungck [13], Matkowski [op. cit.] and some of their generalization, for non continuous systems of maps.


Keywords


Fixed point, coincidence point, Matkowski contraction, product space, reciprocal continuous maps, coordinatewise commuting, weakly commuting, compatible and R-weakly commuting maps.

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